Fluorescence energy transfer is widely used in biochemical research, usually to measure the distance between donors(D) and acceptors(A). A single static D-A distance exists in certain cases, such as a proteins in the native state labeled at two specific locations. A single donor-acceptor distance is not expected in many other cases of interest, such as denatured macromolecules, lipid distributions in membranes, and ion distributions around DNA and other macromolecules. Additionally, diffusive motions can result in time-dependent changes in the donor-acceptor distances. We propose to gegneralize the use of energy transfer to determine the distance probability distribution of donor-acceptor pairs. The information is contained in the time-dependent decays of fluorescence intensity, which will be measured by both time-correlated single photon counting and by frequency-swept (1-200 MHz) phase-modulation fluorometry. We will examine several experimental systems to verify the theory and algorithms which we will develop. These systems are: 1. Simple solutions of charged and neutral donor-acceptor pairs, 2. Donor-acceptor pairs attached to flexible or rigid peptide chains, 3. Donor-acceptor pairs attached to native and denatured ribonuclease, t-RNA, and calmodulin at various ion concentrations, 4. Counterion distributions around DNA, and 5. Lipid distributions in model membranes and around membrane-bound proteins. We will develop the theory needed to interpret the time-resolved parameters of both donor and acceptor fluorescence in terms of the distribution of distances and the time-dependent diffusive changes in the D-A distance. This is of interest for comparison with polymer theory and molecular dynamics. Software will be developed in collaboration with M. Johnson, University of Virginia.